This book is written principally for students of precious stones and jewellers,
and more particularly for diamond manufacturers and diamond cutters and polishers.
The author will follow the evolution of the shape given to a cut diamond,
and discuss the values of the various shapes and the reason for the discarding
of the old shapes and the practically universal adoption of the brilliant.

It is a remarkable fact that, although the art of cutting a diamond has been
known for more than two thousand years, it is entirely empirical, and that,
though many keen contemporary minds have been directed upon the diamond,
and the list of books written on that subject increases rapidly,
yet nowhere can one find any mathematical work determining the best shape
for that gem. The present volume's chief aim is the calculation of that shape.

The calculations have been made as simple as possible, so as not to be beyond
the range of readers with a knowledge of elementary geometry, algebra,
and trigonometry. Where, however, it was found that the accuracy of the results
would be impaired without the introduction of more advanced mathematics,
these have been used, and graphical methods have been explained as an alternative.

The results of the calculations for the form of brilliant now in use were verified
by actual mensuration from well-cut brilliants. The measures of these brilliants
are given at the end of the volume both in a tabulated and in a graphical form.
It will be seen how strikingly near the actual measures are to the calculated ones.

The method used in the present work will be found very useful for the design
of other transparent precious and semi-precious stones, although it will be found
advisable in the case of stones of an agreeable colour to cut the gem somewhat
thicker than the calculations warrant, so as to take full advantage of the colour.
The same remark applies to diamonds of some exceptional and beautiful colour,
like blue or pink, where the beauty or value of the stone increases
with the depth of its colour.